CMB Lensing Amplitude

Gravitational lensing of the CMB by intervening large-scale structure smooths the acoustic peaks and generates a detectable lensing power spectrum. Planck analyses find a lensing amplitude parameter A_lens = 1.18 ± 0.065, meaning the observed lensing is approximately 18% stronger than predicted by the best-fit ΛCDM cosmology derived from the same CMB data — a 2.8-sigma tension that has persisted across data releases. In SCT, the enhanced lensing amplitude is a direct prediction of the gravitational superposition mechanism. When nested comoving frames overlap, their gravitational fields add constructively according to the GR superposition principle. Intermediate-redshift matter — which provides the bulk of the CMB lensing kernel — sits within overlapping gravitational wells from the local frame, the galactic halo, the Local Group, and higher parent frames. This superposed potential is systematically deeper than what the observed baryonic and dark matter mass alone would predict, producing additional convergence along every line of sight.

The enhancement is not uniform: it is stronger along lines of sight passing through dense filaments and cluster intersections, where multiple levels of the frame hierarchy coincide, and weaker through voids where Λ_eff locally suppresses the frame binding. The net effect when averaged over the full sky is an A_lens excess of order 10–20% relative to the particle-counting baseline, consistent with the Planck measurement. This resolution is mutually consistent with the S8 tension resolution: the same gravitational superposition that boosts weak lensing shear signals also boosts CMB lensing, and both excesses share the same underlying GR mechanism without requiring any new physics or particles.